Problem: $f(x) = \dfrac{ x + 8 }{ ( x + 8 )( x - 5 ) }$ What is the domain of the real-valued function $f(x)$ ?
Solution: $f(x)$ is undefined when the denominator is 0. The denominator is 0 when $x=-8$ or $x=5$ So we know that $x \neq -8$ and $x \neq 5$ Expressing this mathematically, the domain is $\{ \, x \in \RR \mid x \neq-8, \,x \neq5\, \}$.